AP Statistics - Chapter 2
Normal Distribution
Name:________
Date:_________
A density curve consists of a straight-line segment that begins at the origin (0, 0) and
has slope 1.
1. Sketch this density curve. What are the coordinates of the right endpoint of the
segment? (Note that the right endpoint should be fixed so that the total area under the
curve is 1. This is required for a valid density curve.)
2. Determine the median, the first quartile (Q1 and the third quartile (Q3).
3. Relative to the median, where would you expect the mean of the distribution to lie?
Explain briefly.
4. What percent of the observations lie below 0.5? Above 1.5?
Runner’s World reports that the times of the finishers in the New York City 10-km run
are normally distributed with a mean of 61 minutes and a standard deviation of 9
minutes.
5. Find the proportion of runners who take more than 70 minutes to finish. Draw a
sketch to show this proportion.
6. Find the proportion of runners who finish in less than 43 minutes. Draw a sketch to
show this proportion.
The Chapin Social Insight Test evaluates how accurately the subject appraises other
people. In the reference population used to develop the test, scores are approximately
normally distributed with mean 25 and standard deviation 5. The range of possible
scores is 0 to 41.
1. If a randomly selected student has a score of 40, then how many standard deviations
away from the mean is that student’s score?
2. Determine the standardized value for the score of 22.
3. What is the relative frequency corresponding to a score of 25 or more?
The Graduate Record Examinations are widely used to help predict the performance
of applicants to graduate schools. The range of possible scores on a GRE is 200 to
900. The psychology department at a university finds that the scores of its applicants
on the quantitative GRE are approximately normal with mean = 544 and standard
deviation = 103. Use Table A to find the relative frequency of applicants whose score
X satisfies the following conditions: (As part of your answer, draw a standard normal
curve and shade the area under the curve that represented the answer to the question.
4. X<500
5. 500<X<700
6. What minimum score would a student need in order to score better than 77% of
those taking the test?